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ArticleOriginal scientific text

Title

The density property for JB*-triples

Authors 1, 1, 1

Affiliations

  1. Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland

Abstract

We obtain conditions on a JB*-algebra X so that the canonical embedding of X into its associated quasi-invertible manifold has dense range. We prove that if a JB* has this density property then the quasi-invertible manifold is homogeneous for biholomorphic mappings. Explicit formulae for the biholomorphic mappings are also given.

Bibliography

  1. S. Dineen and P. Mellon, Holomorphic functions on symmetric Banach manifolds of compact type are constant, Math. Z., to appear.
  2. J. Dorfmeister, Algebraic systems in differential geometry, in: Jordan Algebras, de Gruyter, Berlin, 1994, 9-33.
  3. H. Hanche-Olsen and E. Størmer, Jordan Operator Algebras, Pitman, Boston, 1984.
  4. W. Holsztyński, Une généralisation du théorème de Brouwer sur les points invariants, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 12 (1964), 603-606.
  5. W. Kaup, Algebraic characterization of symmetric complex Banach manifolds, Math. Ann. 228 (1977), 39-64.
  6. W. Kaup, A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces, Math. Z. 138 (1983), 503-529.
  7. W. Kaup, Hermitian Jordan triple systems and automorphisms of bounded symmetric domains, in: Non-Associative Algebra and Its Applications, Kluwer, Dordrecht, 1994, 204-214.
  8. O. Loos, Bounded symmetric domains and Jordan pairs, lecture notes, Univ. of California at Irvine, 1977.
  9. O. Loos, Homogeneous algebraic varieties defined by Jordan pairs, Monatsh. Math. 86 (1978), 107-127.
  10. J.-I. Nagata, Modern Dimension Theory, North-Holland, Amsterdam, 1985.
  11. M. A. Rieffel, Dimension and stable rank in the K-theory of C*-algebras, Proc. London Math Soc. 46 (1983), 301-333.
  12. C. E. Rickart, Banach Algebras, Van Nostrand, Princeton, 1960.
  13. H. Upmeier, Symmetric Banach Manifolds and Jordan C*-Algebras, North-Holland, Amsterdam, 1985.
  14. K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov and A. I. Shirshov, Rings That Are Nearly Associative, Academic Press, 1982.
Studia Mathematica
1999/137/2
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Pages:
143-160
Main language of publication
English
Received
1998-03-11
Accepted
1998-05-12
Published
1999
Exact and natural sciences